ELECTRICAL MACHINES - uotechnology.edu.iq

1 Page | 1 ELECTRICAL MACHINES Notes Dr. AF BATI Page 1 ELECTRICAL MACHINES REFERENCES: 1. D. BROWN & E. P. HAMILTON ELECTROMECHANICAL ENERGY CONVERSION MACMILLAN, NY 1984. 2. H. COTTON ADVANCED ELECTRICAL TECHNOLOGY PITMAN, LONDON 1967. 3. A. R. DANIELS INTRODUCTION TO ELECTRICAL MACHINES MACMILLAN, LONDON 1976. 4. A. DRAPER ELECTRICAL CIRCUITS INCLUDING MACHINES LONGMAN, LONDON 1972. 5. A. DRAPER ELECTRICAL MACHINES 2ND EDITION, LONGMAN ,LONDON. 6. A. E. FITZGERALD, D. E. HIGGINBOTTOM ,& A. GABRIEL BASIC ELECTRICAL ENGINEERING 5TH ED. MCGRAW HILL, NY 1981. 7. A. E. FITZGERALD, C. KINGSLEY, & S. D. UMANS ELECTRICAL machinery , 4TH ED. MCGRAW HILL, TOKYO 1983. 8. J. HINDMARSH ELECTRICAL MACHINES AND THEIR APPLICATIONS 4TH ED.

2 PERGAMON, OXFORD 1984. 9. E. HUGHES ELECTRICAL TECHNOLOGY LONGMANS, LONDON. 10. G. MCPHERSON AN INTRODUCTION TO ELECTRICAL MACHINES and transformers WILEY, NY 1981. 11. S. A. NASAR electric MACHINES AND ELECTROMECHANICS MCGRAW HILL(SCHAUM), NY 1981. 12. S. A. NASAR & L. E. UNNEWEHR ELECTROMECHANICS AND electric MACHINES , 2ND ED. WILEY, NY 1983. 13. J. ROSENBLATT & M. H. FRIEDMAN DIRECT AND ALTERNATING CURRENT machinery 2ND ED. MERRILL, COLOMBUS OHIO 1984. 14. Theraja Bl, Theraja Ak ELECTRICAL TECHNOLOGY . 15. A. S. LANGSDORF THEORY OF ALTERNATING CURRENT machinery 2ND ED. MCGRAW HILL, NY 1955. DC MACHINES ONLY : 16. A. E. CLAYTON & N. M. HANCOCK THE PERFORMANCE AND DESIGN OF DIRECT CURRENT MACHINES 3RD ED. PITMAN, LONDON 1959. 17. M. G. SAY & E. O. TAYLOR DIRECT CURRENT MACHINES PITMAN, LONDON 1980. Page | 2 ELECTRICAL MACHINES Notes Dr.

3 AF BATI Page 2 CHAPTER 1 : PRINCIPLE OF OPERATION SOME BASIC RULES Right hand screw rule (cross product operation in vector algebra) A1 X A2= A3 A1, A2, and A3 are vectors. Rotate RH fingers from the direction of the first vector , A1, to the direction of the second vector, A2, through the small angle (<180o) between them; the direction of A3 is then given by the extended RH thumb. In our applications, the magnetic field B is always the second vector. Given a straight conductor lying in a magnetic field, and oriented perpendicular to the direction of the field. Let B= magnetic flux density (also called magnetic induction), [T=tesla=weber/m2]; L=active length of conductor,[m]. u Induced voltage (emf): E= volts u= speed of conductor perpendicular to its length[m/s]; = small angle from u to B.

4 Direction of E : RH screw rule from u to B . Developed force : Fd= newtons [N] I= current through conductor, [A]. Direction of Fd : RH screw rule from I to B. Page | 3 ELECTRICAL MACHINES Notes Dr. AF BATI Page 3 Single conductor Consider a straight conductor moving at a uniform speed u in a uniform magnetic field B, and carrying a current I. Let L= active length( length of conductor segment immersed in the field); Fm= applied mechanical force, [N]. u & B give E= and I & B give Fd= ( ).I=( ). u= Fd. u Pc = conversion power Note: Because the speed u is constant, Fd and Fm must be equal and opposite( otherwise there would be acceleration or deceleration). is ELECTRICAL power , and Fd.

5 U (Fm. u) is mechanical power. I in direction of E; Fd opposite to u. I opposite to E; Fd in Direction of u. Generation action. Motor action Page | 4 ELECTRICAL MACHINES Notes Dr. AF BATI Page 4 V=E V=E + tSFtWPmmin = = Pin= (E+ ). I = Fd. u= Pc = + Pc+Pcu Pcu= copper losses Pout= (E ).

6 I Pout= tSFtWmm = = Pc Pcu =Fd. u= Pc = Pin Pcu Pin= Pout + Pcu Pin Pout= Pcu Pin Pout = Pcu Wire loop Consider now a wire loop rotating at a uniform speed in a magnetic field B. Conductors a and b are the active parts of the loop; the remaining parts are end connections and leads . Page | 5 ELECTRICAL MACHINES Notes Dr. AF BATI Page 5 Fda = Fdb zero resultant force Td= developed torque i in direction of e ; Td opposes rotation i opposes e; Td aids rotation Generator action.

7 Motor action. KVL: e= ea + eb = loop emf Slip rings Slip rings and brushes may be used to make ELECTRICAL contact with a rotating loop. Slip rings rotate with loop , while brushes are stationary to give sliding contact. A slip ring and a brush for each terminal. Page | 6 ELECTRICAL MACHINES Notes Dr. AF BATI Page 6 The induced emf is alternating, and the developed torque oscillates (about the vertical position). Clearly, slip rings are not suitable for dc MACHINES (they are used in ac MACHINES ). Commutator A commutator is a conducting ring split into segments; each segment is electrically connected to one terminal of the loop. It is mounted on the shaft , but is electrically insulated from it. The brushes are stationary and make sliding contact with the segments.

8 A2 is always positive; A1 is always negative: >>> et is always positive , & Td is always CW(when direct current supplied to brushes), but emf & current within loop oscillate. Although et and Td are now unidirectional ( remain in the same direction or sense), they do not represent steady dc operation because they fluctuate: each is maximum when the loop is in posi on 0 , and zero when it is in posi on 2. Multiple loops More uniform dc operation is achieved by using a number of loops displaced from each other in space. The emf s add (series connection), and the developed torques aid each other. As the number of loops is increased, ideal dc operation is approached. Page | 7 ELECTRICAL MACHINES Notes Dr. AF BATI Page 7 2 loops 4 loops Magnetic circuit The magnetic field may be obtained by means of permanent magnets (PM), or, more commonly, by means of electromagnets (field coils with iron cores).

9 Permanent magnet electromagnet practical construction (with soft iron extension) The value of the resulting flux is determined by the mmf (magnetic motive force) ( of the PM or electromagnet) and the magnetic reluctance in the path of the flux. Iron has very high magnetic permeability, so that it is the air gap in the path of the flux that limits its value. The air gap must therefore be made short to increase the effective flux. The air gap cannot be avoided completely(why?) . Page | 8 ELECTRICAL MACHINES Notes Dr. AF BATI Page 8 Air core cylindrical iron core slotted iron core(armature) Multiple poles A dc machine can have 2,4,6,8,.. Poles(an even number why?)

10 2p=number of poles; ( p=number of pole pairs) One revolu on=360 mechanical degrees; One pole pair= 360 ELECTRICAL degrees; ELECTRICAL angle=p X mechanical angle; Pole pitch =180o ELECTRICAL = 360o mech/2p . Each armature loop is placed over one pole pitch. Electrically, every thing repeats after two pole pitches. loop emf D= diameter of the armature[m]; L=active length of armature[m]; n= rotational speed [rps=revolution per second]; u= speed= Dn [m/s]; r=angular speed= 2 n [rad/s]. Ap=armature surface area corresponding to one pole pitch= DL/2p [m2]. = flux per pole [wb=weber]; total magnetic flux through pole face: same for all poles; B = air gap flux density [T=tesla=wb/ m2]; normal field at armature surface; Bav = ave = Ap B. The actubelow. Twire loopea= averEa= Bav. L Stator(fie Air gap Motion> Rotor (armatur Elerage air gapdA ; Bav= al air gap fluhe average gp; the instan (ea (t) haage emf ( constaeld) >>> B re) ectrical Mach flux density /Ap ux density B gap flux denntaneous emas the same uced in sideant over altehines Notes y [T].))